If ABCD is a proportional line segment, does it mean a: B = C: D or a: C = B: D but not a: D = B: C

If ABCD is a proportional line segment, does it mean a: B = C: D or a: C = B: D but not a: D = B: C

ABCD is a proportional line segment, which means a: B = C: D attention order
a: C = B: D is the deformation of a: B = C: D
But we can't get a: D = B: C

Given the line segments a, B, C, D (B ≠ d), if a / b = C / D = k, then a-c / B-D = a + C / B + D why?

∵a/b=c/d=k
∴a=bk c=dk
∴a-c/b-d=bk-dk/b-d=k
a+c/b+d=bk+dk/b+d=k
∴a-c/b-d=a+c/b+d
The conclusion is proved
In the future, when we meet this kind of problem, we will express the relationship between different letters with K. if there is no K, we will set one. The basic method of doing proportion problem is to set k every time

Four line segments ABCD are proportional, where a = 12cm, B = 3cm, C = 4cm, find the length of line segment D
Find all the values of D

Three possibilities
ad=bc
Then 12D = 12
d=1
ab=cd
Then 36 = 4D
d=9
ac=bd
Then 48 = 3D
d=16

How many times is BC equal to ab if four points ABCD are successively arranged on a straight line, and point C is the midpoint of line ad, BC minus AB equals one fourth of ad?

AB+BC=AC=1/2AD
BC-AB=1/4AD
Two style simultaneous
BC=3/8AD
AB=1/8AD
So BC is three times of ab

In a pyramid p-abcd, if the PD ⊥ surface ABCD, the bottom surface ABCD is a rectangle, ab = 2, M is a point on the line AB, and cm ⊥ PM, the length range of the line BC is obtained

Let the range be x, then x = root sign (2Y - y × y) y belongs to 0 to 2, open interval, and the result obtained by limit is 0 to 1, open interval

It is known that, as shown in the figure, in the quadrilateral ABCD, ∠ B + ∠ d = 180 °, ab = ad, e and F are the points on the line BC and CD respectively, and be + FD = EF

It is proved that: rotate △ ADF clockwise around point a to get △ ABG, ad rotates to AB, AF rotates to Ag, as shown in the figure, ∧ Ag = AF, BG = DF, ∧ ABG = ∧ D, ∧ bag = ∧ DAF, ∧ B + ∧ d = 180 degree, ∧ B + ∧ ABG = 180 degree, ∧ points g, B, C are collinear, ∧ be + FD = EF, ∧ be + BG = Ge = EF, in △ AEG and △ AEF, Ag = AFAE = AEEG = EF, ≌ AEG ≌ AEF, ∧ EAG = EAF And ∠ bag = ∠ DAF, ｜ ∠ EAB + ∠ DAF = ∠ EAF, ｜ ∠ EAF = 12 ∠ bad

As shown in the figure, in rectangular ABCD, ab = 3, BC = 1, e is the moving point on the line DC, now fold △ AED along AE to make plane AED ⊥ plane ABC, pass through point D in plane AED to make DK ⊥ AE, K is perpendicular foot, when e moves from D to C, the length of the track formed by K is______ ．

According to the meaning of the title, the △ AED is folded along AE to make the plane AED ⊥ plane ABC, passing through point d to make DK ⊥ AE in the plane AED, and K is the perpendicular foot. According to the folding characteristics, if d'k is connected, then d'ka = 90 degrees, so the trajectory of point K is an arc on a circle with diameter ad '. It is easy to know that the radius of this circle is 12. As shown in the figure, when E and C coincide, AK = 1 × 14 = 1

Given that a: B: C: D is a proportional line segment, can the position of ABCD be changed?

I can't
It's different when you exchange the meaning

It is known that ABCD is a proportional line segment, and a = 5, B = 6, C = 20, d =?

a:b=c:d
bc=ad
d=24

Is there an order in which the four line segments ABCD are proportional

Orderly
a:b=c:d.